Van Aubel's theorem

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The theorem can be applied to a complex (self-intersecting) quadrilateral.

In geometry, Van Aubel's theorem describes a relationship between squares constructed on the sides of a quadrilateral. Starting with a given quadrilateral (a polygon having four sides), construct a square on each side. Van Aubel's theorem holds that the two line segments between the centers of opposite squares are of equal lengths and are at right angles to one another. Another way of saying the same thing is that the center points of the four squares form the vertices of an equidiagonal orthodiagonal quadrilateral. The theorem is named after H. H. van Aubel, who published it in 1878.[1]

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Notes[edit]

  1. ^ van Aubel, H. H. (1878), "Note concernant les centres de carrés construits sur les côtés d'un polygon quelconque", Nouvelle Correspondance Mathématique (In French) 4: 40–44 .

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